SOLUTION: A rectangular prism has base dimensions of 24 cm by 7 cm. A metal rod is run from the bottom corner diagonally to the top corner of the prism. If the rod forms an angle of 40 with
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Question 1105247: A rectangular prism has base dimensions of 24 cm by 7 cm. A metal rod is run from the bottom corner diagonally to the top corner of the prism. If the rod forms an angle of 40 with the bottom of the box, calculate the volume of the box. Answer by greenestamps(13203) (Show Source):
The bottom of the box has dimensions 24cm by 7cm. The diagonal of the bottom of the box, by the Pythagorean Theorem, has length 25cm.
The 40 degree angle is formed by the bottom of the box, the rod, and the height of the box, with the rod being the hypotenuse of the right triangle. Then
The volume of the box is
If you need a more accurate answer you can keep more digits of tan(40).
